Campus Livre
chebyshevU
Chebyshev polynomial of the second kind.
Category: Mathematics > Polynomials
Syntax
P = chebyshevU(n, x)Evaluates the Chebyshev polynomial of the second kind of degree n at x.
Description
U_n(x) is defined by U_n(cos(theta)) = sin((n + 1)*theta)/sin(theta). It obeys the same recurrence as T_n, U_(n+1) = 2*x*U_n - U_(n-1), but starts from U_0 = 1 and U_1 = 2*x. It is orthogonal on [-1, 1] with the weight sqrt(1 - x^2).
The two kinds are linked by T_n'(x) = n*U_(n-1)(x).
Input arguments
n- Degree, a nonnegative integer or a symbolic variable.
x- Point(s) of evaluation, or a symbolic variable to get the polynomial.
Output arguments
P- Numbers with the size of
x, or a symbolic polynomial.
Example
Degree 2 to 4
syms x
chebyshevU(2:4, x)
chebyshevU(2, 0.5)Output
ans =
[4*x^2 - 1, 8*x^3 - 4*x, 16*x^4 - 12*x^2 + 1]
ans = 0